Scottish First Minister Nicola Sturgeon has rejected the UK government's latest proposal in a row over who should exercise certain powers after Brexit.
Cabinet Office Minister David Lidington said the "vast majority" of returning EU powers will start in Edinburgh, Cardiff and Belfast.
He said Westminster would only be involved where a "pause" was needed to draw up a UK-wide framework.
But Ms Sturgeon said this would still restrict the devolved administrations.
It amounts to a veto over how the Scottish Parliament and the Welsh and Northern Ireland assemblies can exercise their powers, she told the BBC.
Ms Sturgeon said it was "very likely" the Scottish Parliament will not give consent for the EU Withdrawal Bill unless the UK government changes its mind.
The move would not veto or block Brexit, but would make things extremely difficult politically for the prime minister.
The two governments have been at loggerheads over how powers which are currently not reserved to Westminster, but which are exercised from Brussels, are distributed after the UK leaves the EU.
Ms Sturgeon said she accepted that in some cases there would need to be common systems of regulation, but she insisted that they needed to be agreed between the UK government and the devolved administrations - and cannot be imposed by Westminster.
She said: "We are simply trying to protect the powers that the Scottish Parliament already has - things like agriculture, fishing, environmental policy, food standards, justice, health.
"These are all currently responsibilities of the Scottish Parliament. At the moment we have to exercise those powers within the confines of European law.
"But after Brexit, in terms of the devolution settlement, those powers should return to the Scottish Parliament and it should be up to us how we exercise them."
On Monday, Mr Lidington said the UK's "common market" must be maintained post-Brexit, saying the UK works better in "unity".
Food labelling and hygiene rules were one area where powers could be retained within a UK-wide framework, Mr Lidington suggested.
He added that the government had made a "considerable offer" to the devolved administrations.
Analysis by Brian Taylor, BBC Scotland political editor
Let's be clear - the devolved administrations cannot veto Brexit, they cannot block, they cannot thwart.
The talk of there being a requirement for consent from the Scottish Parliament, Welsh Assembly and Northern Ireland Assembly is purely a convention, and hasn't got weight in law.
Westminster is sovereign, and Westminster can legislate in this matter.
If Westminster wants, it can say: "If we can get this EU Withdrawal Bill through the House of Commons and through the House of Lords, then that's good enough for us and the rest of you can go swing."
But Westminster will not do that. Why? Because they want to proceed by consensus. The UK government is in enough trouble over Brexit without adding a fight with Holyrood into the mix as well.
Ms Sturgeon said her government had always accepted there were issues where it makes sense to have common standards and regulations in all parts of the UK.
But she said the UK government proposals meant Holyrood would have no say over any attempt by Westminster to lower environmental standards in Scotland - despite the powers being devolved.
The first minister added: "I will not sign up to something that effectively undermines the whole foundation on which devolution is built and no first minister, no Scottish government worth its salt, should do so."
She denied she was using the row as an excuse to push for independence, and insisted that the Scottish government was trying to reach agreement.
But she said that, as things currently stand, it was "very likely" that both the Scottish and Welsh governments would ask their respective parliaments to not recommend approval of the EU Withdrawal Bill.
Talks are continuing as the EU Withdrawal Bill makes its way through the House of Lords.
The bill aims to ensure the rules currently set by European law still apply in the UK after Brexit, while giving the UK Parliament power to change them.
The Scottish government is expected to introduce its own EU Continuity Bill at Holyrood this week.